Brutal Game!

Logic Level 3

100 people are standing in a circle. The first person has sword in his hand. He kills the second person and hands over the sword to the third person. Then the third person does the same. This goes on and on until one person is left. At which place is he(alive person) stand.


The answer is 73.

View wiki
Rishabh Jain by Rishabh Jain , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Arun Damodaran
Jul 7, 2015

Well this one is most frequently asked one, however I try to make approach simple: - One in every two person dies! so here we should be careful while modelling the problem

  • Basic Sense is that if the total number (N) is a power of 2 then the FIRST one to start never dies!

  • So get a number k=Power of 2 as well as nearer to total number (N) in this case N=100. Thus k=64.

  • Thus for 64 people to remain we have to kill 36 people. which will map to 72

  • because @ first go , all even no's will die!

  • The next no i.e. 73 will become new NO.1 and total number of people will be 64(a power of two).

  • Thus 73 is the person that ll survive.

  • Well

  • here's something good!
  • It has a formula : 2*(N-2^{k})+1
  • where N----> total people
  • 2^{k}------> is power of two equal to or less than N
3 Helpful 0 Interesting 0 Brilliant 0 Confused

I understand this explanation less than the actual problem. Can someone please clarify this for me? I did get 73, but had to count my way through it.

Michael Worthley-Seldon - 5 years, 8 months ago

Log in to reply

  • Consider there are 4(which is a pow of 2 ) people 1,2,3,4
  • If 1 starts to kill after two rounds 1 will remain after 1 kills 2------->3 kills 4------->1 kills 3
  • So the conclusion is if the number is power of 2 the first person to start will remain till the end
  • If a number N is not a power of 2 then search for a number P nearest to N which is of course a power of 2.
  • Wait till (N-P) deaths occur then the next person immediate to hold the sword lives!
  • I think I have done justice! Please notify if not understood

Arun Damodaran - 5 years, 8 months ago
E Koh
Oct 29, 2019

Here, we can define an array with 100 elements with values from 1 to 100. No.1 has a sword. He kills next person (i.e. no. 2) and gives sword to next to next (i.e no. 3). We have taken array element as a person. 1st person kills the next. So, starting from 1, we’ll remove next element i.e. 2. Then first person gives sword to next to next i.e. 3. That person will also kill next person and this continues. Means, in array, we need to start with 1 and remove the every other (alternate) element till 100. (all the even numbers will be removed and we’ll be left with odd numbers only in array). Round 1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99 Round 2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97 Round 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97 Round 4: 9, 25, 41, 57, 73, 89 Round 5: 9, 41, 73 Round 6: 9, 73 Round 7: 73

The solution requires getting the nearest smaller number that is the power of 2, in this case 64 and subtract it with the given number.100-64=36. Now we apply the formula; 2n+1 = 2*36 + 1 = 72 + 1 = 73.

Hence answer = 73

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...